Downlink (DL) multi-user multiple-input multiple-output (MU-MIMO) transmission methods are well-known in the art. These DL MU-MIMO transmission methods rely on knowledge of the channel at the transmitting base station (BS), or, more precisely, the availability of estimates of the channels between the BS antennas and the user terminals (UTs) to which this BS is transmitting information. This channel state information is then used to “precode” the information intended for each of the UTs prior to transmission, in such a way, that each of the UTs is able to decode the signals of its own interest.
The necessary channel state information is obtained by transmitting pilots (i.e., known signature waveforms) over wireless medium and estimating these channels based on the received waveforms. Then these estimates are used for generating the MU-MIMO precoder (i.e., the transmission method) and for transmitting data to the UTs. Since the channels change over time (and frequency), the process of training is repeated periodically across the network. In what are referred to as “pilot-on-pilot” schemes, the pilot transmission cycles are aligned in time across all BSs, while in pilot-on-data schemes the pilot transmission cycles of a given BS overlap with data transmissions from other BSs. The fraction of time (or time-frequency slots) allocated to a single training session dictates the number of channel uses allocated for pilot training to each BS. The dimensionality of this “pilot-training” signal space places a constraint on the number of possible orthogonal (or, linearly independent) pilots that can be signaled during each training phase. Given that the number of BS-UT channels that need to be obtained across the whole network is well beyond the channel uses allocated for training in each cycle, or equivalently well beyond the number of allotted signal space dimensions for pilot training, pilots have to be reused across the network.
There are two classes of training methods used in DL MU-MIMO for obtaining channel estimates at the transmitting BS. The two classes are effectively distinguished by the parties that transmit the pilots. In what are referred to as FDD-based training schemes, to estimate the channels between the BS and each of the UTs, pilots are first transmitted by the BS. Each UT then collects measurements of the transmitted pilots and estimates its own channels. Then over a shared channel on another frequency band, the UTs communicate (feed back) these estimates to the BS in their cell.
In what are referred to as TDD-based training schemes, estimates of the channels from each UT to its transmitting BS are obtained directly at the BS, by transmitting pilots from each of the UTs. These schemes rely on the notion of “channel reciprocity,” which states that the channel from a BS to a UT on a given band and at a given time instance is the same as, or more accurately, correlated to the channel from the UT to the BS on a possibly different band and at a possibly different time instance, provided the gaps in time-instances and frequency-bands of the two channels are within the channel coherence time and bandwidth, respectively. These schemes rely on sending pilots in the uplink from a set of UTs, collecting measurements at the BS, estimating the BS-UT channels based on these measurements at the BS, and then performing MU-MIMO transmission from the BS to the UTs over the same band and within the channel coherence time.
Reducing the spatial reuse factor of the pilots reduces the number of pilots that need to be signaled within each training cycle. It thus reduces the pilot overhead and allows more slots to be used for data transmission. However, the need for reusing pilots spatially in all these training schemes comes at a cost in channel estimate quality. Consider estimating a channel between a BS and a UT in its cell by means of a given pilot (from a set of orthogonal pilots). UTs throughout the network using the same pilot interfere or “contaminate” the estimates between the BS and UT of interest. Typically, the closest the interfering UT is to the BS of interest, the largest the “pilot contamination” levels. As a result, reducing the pilot spatial reuse factor can be used to either increase the fraction of time dedicated to data transmission or increase the number of simultaneously trained users. However, in both cases, it also increases the levels of pilot contamination and can thus reduce the efficiency of the data transmission cycle.
DL MU-MIMO schemes with TDD based training can often provide advantages with respect to their FDD based counterparts. In particular, assume that a fixed number of users S(t) are served in each active cell within a given scheduling slot t (whereby a scheduling slot comprises a set of time-frequency slots comprising one or more RBs). In TDD-based training schemes, increasing the number of transmit antennas per BS, while keeping S(t) fixed, does not change the training scheme and thus the training overhead. On the other hand, increasing the number of transmit antennas strictly improves the rates provided by the MU-MIMO scheme to each of the S(t) users served in each cell by the scheme. Although such increases in rate are also present in the data-transmission portion of FDD-based DL MU-MIMO, in FDD such higher-throughput transmissions from larger antenna arrays come at a cost of increased training overheads.
Subject to a limit on the number of time-frequency slots allocated for training within a scheduling slot, DL MU-MIMO schemes with reciprocity-based training can leverage the use of large antenna-arrays to provide high net cell throughput. However, if the system is not properly designed, the scheme can yield very unfair user rate distribution across the cellular deployment.
Consider the basic setting in which any given cell assigns its pilots randomly to its UTs within the cell, and independently of other cell pilot assignments. In such a setting, the uplink pilot transmitted by any one of the UTs experiences pilot contamination whose power may take values over a possibly wide range, depending on the locations (and the transmit powers) of the UTs re-using this pilot in neighboring cells. To be more specific, in DL MU-MIMO schemes with TDD-based training, the pilot contamination caused by the reuse of a pilot in a neighboring cell strongly depends on which UT has been assigned the same pilot in the neighboring cells. In particular, the quality of the estimate of the channel between a BS and a UT in its cell, obtained by a TDD-based training scheme, depends on the following quantities:                The large-scale power attenuation affecting transmissions from the UT to the BS, and the effective pilot transmit power; these dictate the power of the “useful pilot signal” component in the measured signal that is used for channel estimation at the BS of interest; and        The large-scale power attenuation affecting transmissions from the UTs re-using the same pilot (in neighboring cells) to the BS of interest, and the associated transmit powers in these pilots; these dictate the power of the interference or pilot-contamination signal component in the measured signal that is used for channel estimation at the BS of interest.        
The value of any such large-scale signal-strength quantity is affected by several factors, including distance between the transmitting and receiving parties, shadowing, and other environmental factors. Knowing these quantities, would allow the BS to optimally use the measurements in forming its channel estimate so as to maximize the estimate quality.
The BS may not in general possess knowledge of the interference level experienced by each of the pilots used by its UTs. In that case, it would have to be conservative in forming its estimates (i.e., it would have to assume the highest possible level or a very high level among the possible interference levels). This can result in a significant reduction of the channel estimate quality.
In order to gain some appreciation for the effects of the pilot contamination on the rates provided to UTs as a function of their location, in architectures employing MU-MIMO with reciprocity based-training, it is worth considering one well-known scheduling/training MU-MIMO scheme for DL transmission. This scheme uses very simple (random) scheduling assignments. It also uses very simple (random) training sequence assignments. The first half of the time-frequency slots within a scheduling slot are dedicated to training, and within each active cell each of the users is randomly assigned a training slot. The scheme also relies on trivial MU-MIMO precoders. In particular, during the downlink transmission (the second half of the scheduling slot), the BS linearly superimposes the signals that are intended to the scheduled users it each cell and transmits them. The signal transmitted by any given antenna to a given user in any given time-frequency slot within the scheduling slot is simply a scalar coded UT stream sample, scaled by the conjugate of channel estimate between this antenna and the UT antenna. As a result, this precoder schedules each UT on a precoding vector/beam that is the conjugate of the channel estimate between the TX antenna array and the (same) UT antenna. This precoder is commonly referred to as a linear single-user beamforming (LSUBF) precoder. The precoding vector for any given UT is selected simply as the beam that is beamforming at the UT. Note that in selecting a beam for a particular UT, this precoder makes no “multi-user” considerations or provisions, i.e., it does not take into account the interference caused by the beam to other UTs in the system.
This scheme enables high edge and center user rates by leveraging reuse-7 and enormous numbers of antennas. Although reuse-7 is highly inefficient, it is necessary in this scheme to bring edge user rates to respectable levels. To see this, consider a reuse-1 system. Because users in each cell are selected at random for transmission and pilots are reassigned in each cell randomly, it is possible that the received pilot strength at a BS from a user in its cell is lower than the aggregate received interference power, arising from all users in neighboring cells using the same pilot. As a result, the pilot contamination levels for such a user would be overwhelming, effectively resulting in zero-rate transmission to these users.
Note that, even if higher pilot reuse factors were employed in such a scheme to enable reuse-1 cellular transmission, the choice of such elementary precoder limits the net cell throughput rates. In particular, it is well known that for users in the center of a cell using precoders that also account for multi-user interference would improve performance.
As a result, there is evidently potential for improving the performance of TDD-based DL MU-MIMO schemes for cellular and beyond deployments by using UT-specific training and transmissions schemes.